Modelling forest dynamics: A perspective from point process methods

Biometrical Journal

Volumn 49, Issue 2, 2007, Pages 176-196

  Comas, Carlos ^a   Mateu, Jorge ^b  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b UNIVERSITAT JAUME I   (Spain)

Author keywords

Correlation functions; Forest dynamics; Forest modelling; Marks; Point processes; Ripley's K; Second order characteristics

Indexed keywords

DYNAMICS; RANDOM PROCESSES; SPATIAL VARIABLES MEASUREMENT; STOCHASTIC SYSTEMS;

CORRELATION FUNCTION; FOREST DYNAMICS; FOREST MODELLING; MARK; MARKED POINT PROCESS; POINT PROCESS; PROCESS-MODELS; RIPLEY'S K; SECOND ORDERS; SECOND-ORDER CHARACTERISTIC;

FORESTRY;

EID: 34247370987     PISSN: 03233847     EISSN: 15214036     Source Type: Journal    
DOI: 10.1002/bimj.200510268     Document Type: Review

References (112)

1. Aber, J. D., Melillo, J. M., and Federer, C. A. (1982). Predicting the effects of rotation length, harvest intensity, and fertilization on fiber yield from northern hardwood forests in New England. Forest Science 28, 31-45.
2. Aldrich, P. R., Parker, G. R., Ward, J. S., and Michler, C. H. (2003). Spatial dispersion of trees in an old-growth temperate hardwood forest over 60 years of succession. Forest ecology and management 180, 475-491.
3. Avery, T. E. and Burkhart, H. E. (1983). Forest Measurements. McGraw-Hill, New York.
4. Baddeley, A. J. and van Lieshout, M. N. M. (1995). Area-interaction point process. Annals of the Institute of Statistical Mathematics 47, 601-619.
5. Batista, J. L. F. and Maguire, D. A. (1998). Modeling the spatial structure of tropical forests. Forest Ecology and Management 110, 293-314.
6. Bella, I. E. (1971). A new competition model for individual trees. Forest Science 17, 364-372.
7. Berger, U. and Hildenbrandt, H. (2000). A new approach to spatially explicit modelling of forest dynamics: spacing, ageing and neighbourhood competition of mangrove trees. Ecological Modelling 132, 287-302.
8. Biging, G. S. and Dobbertin, M. (1995). Evaluation of compettion indices in individual tree growth models. Forest Science 41, 360-377.
9. Botkin, D. B., Janak, J. F., and Wallis, J. R. (1972). Some ecological consequences of a computer model of forest growth. Journal of Ecology 60, 849-873.
10. Botkin, D. B. (1993). Forest Dynamics: An Ecological Model. Oxford University Press, Oxford and New York.
11. Camarero, J. J., Gutiérrez, E., and Fortin, M. J. (2000). Spatial pattern of subalpine grassland ecotones in the Spanish Central Pyrenees. Forest Ecology and Management 134, 1-16.
12. Chapman, D. G. (1961). Statistical problems in dynamics of exploited fisheries populations. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (Vol. 4), Berkeley: University of California Press.
13. Chen, J. and Bradshaw, G. A. (1999). Forest structure in space: a case study of an old growth spruce-fir forest in Changbaishan Natural Reserve, PR China. Forest Ecology and Management 120, 219-233.
14. Clark, P. J. and Evans, F. C. (1954). Distance to the nearest neighbor as a measure of spatial relationships in populations. Ecology 35, 445-453.
15. Comas, C. (2005). Modelling Forest Dynamics Through the Development of Spatial and Temporal Marked Point Processes. University of Strathclyde, Ph.D. Thesis (unpublished).
16. Comas, C. and Mateu, J. (2005). Space-time clustering of reproducing individuals: a perspective from forest dynamics. Research Report 92. Universitat Jaume I, Castellon, Spain.
17. Cox, D. R. (1955). Some statistical methods connected with series of events. Journal of the Royal Statistical Society B 17, 129-164.
18. Cressie, N. (1993). Statistics for Spatial Data. John Wiley and Sons, New York.
19. Degenhardt, A. (1999). Description of tree distribution and their development through marked Gibbs processes. Biometrical Journal 41, 457-470.
20. Degenhardt, A. and Pofahl, U. (2000). Simulation of natural evolution of stem number and tree distribution pattern in a pure pine stand. Environmetrics 11, 197-208.
21. Diggle, P. J. and Milne, R. K. (1983). Bivariate Cox processes: some models for bivariate spatial point patterns. Journal of the Royal Statistical Society B 45, 11-21.
22. Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns. Hodder Arnold, London.
23. Ek, A. R. and Monserud, R. A. (1974). FOREST: a computer model for simulating the growth and reproduction of mixed-species forest stands. Research Paper, R2635 University of Wisconsin.
24. Fiksel, T. (1984). Estimation of parametrized pair potentials of marked and nonmarked Gibbsian point processes. Elektronische Informationsverarbeitung und Kybernetik 20, 270-278.
25. Ford, E. D. and Diggle, P. J. (1981). Competition for light in a plant monoculture modelled as a spatial stochastic process. Annals of Botany 48, 481-500.
26. Ford, E. D. and Renshaw, E. (1984). The interpretation of process from pattern using two-dimensional spectral analysis: modelling single especies patterns in vegetation. Vegetatio 56, 113-123.
27. Gadow, K. V. and Hui, G. Y. (1998). Modelling Forest Development. Series on Forestry Science, Kluwer Academic Publishers.
28. Gadow, K. V. and Hui, G. Y. (2002). Characterising forest spatial structure and diversity. In Bjoerk, L. (ed.), Proceedings IUFRO International Workshop on "Sustainable forestry in temperate regions", Lund, Sweden.
29. Gavrikov, V. L., Grabarnik, P., and Stoyan, D. (1993). Trunk-top relations in a Siberian pine forest. Biometrical Journal 35, 487-498.
30. Gavrikov, V. L. (1995). A model of collisions of growing individuals: a further development. Ecological Modelling 79, 59-66.
31. Gavrikov, V. L. and Stoyan, D. (1995). The use of marked point processes in ecological and environmental forest studies. Environmental and Ecological Statistics 2, 331-344.
32. Gerrard, D. J. (1969). Competition quotient - a new measure of the competition affecting individual forest trees. Agricultural Experiment Station Research Bulletin 20, Michigan State University.
33. Gregori, P. and Mateu, J. (2004). Practical Monte Carlo Maximum Likelihood Estimation for generalised area-interaction models. Proceedings of the XXVIII Meeting of the Spanish Statistical Society, 319-320.
34. Gregori, P., van Lieshout, M. N. M., and Mateu, J. (2004). Mixture formulae for shot noise weighted point processes. Statistics and Probability Letters 67, 311-320.
35. Hasenauer, H. (1994). Ein Einzelbaumwachstumssimulator für ungleichaltrige Fichten- Kiefern- und Buchen-Fichtenmischbestände. Forstliche Schriftenreihe der Universität für Bodenkultur. Wien. Band 8, 152 p.
36. Hasenauer, H., Moser, M., and Eckmüllner, O. (1995). MOSES: a computer simulation program for modelling stand response. In Pinto da Costa, M. E., and Preuhsler, T. (eds.) Mixed Stands, Research Plots, and Results, Models, Instituto Superior de Agronomia, Universidade Technica de Lisboa, Portugal.
37. Heikkinen, J. and Arjas, E. (1999). Modeling a Poisson forest in variable elevation: a nonparametric Bayesian approach. Biometrics 55, 738-745.
38. Kellomäki, S. and Nevalainen, T. (1983). On relationship between stand density and tree size. Silva Fennica 17, 389-402.
39. Kolström, T. (1998). Ecological simulation model for studying diversity of stand structure in boreal forest. Ecological Modelling 111, 17-36.
40. König, G. (1835). Die Forst-Mathematik. Beckersche Buchhandlung, Gotha.
41. Krebs, C. J. (1998). Ecological Methodology: Second Edition. Addison Wesley Longman, Menlo Park, California.
42. Leemans, R. (1991). Canopy gaps and establishment patterns of spruce (Picea abies (L.) Karst.) in two old-growth coniferous forest in Central Sweden. Vegetation 93, 157-165.
43. Mateu, J., Usó, J. L., and Montes, F. (1998). The spatial pattern of forest ecosystems. Ecological Modelling 108, 163-174.
44. Moeur, M. (1993). Characterizing spatial patterns of trees using stem-mapped data. Forest Science 39, 756-775.
45. Moeur, M. (1997). Spatial models of competition and gaps dynamics in old-growth Tsuga heterophylla/Thuja plicata forests. Forest Ecology and Management 94, 175-186.
46. Møller, J., Syversveen, A. R., and Waagepetersen, R. P. (1997). Log Gaussian Cox processes: a statistical model for analysing stand structural heterogeneity in forestry. In Kure, H., Thysen, I. and Kristensen, A. R. (eds.) Proceedings First European Conference for Information Technology in Agriculture pp. 339-342. Department of Mathematics and Physics, Royal Veterinary and Agricultural University, Denmark.
47. Møller, J., Syversveen, A. R., and Waagepetersen, R. P. (1998). Log Gaussian Cox processes. Scandinavian Journal of Statistics 25, 451-482.
48. Monserud, R. A. and Sterba, H. (1996). A basal area increment model for individual trees growing in even-and uneven-aged forest stands in Austria. Forest Ecology and Management 80, 57-80.
49. Motta, R. and Edouard, J. L. (2005). Stand structure and dynamics in a mixed and multilayered forest in the Upper Susa Valley, Piedmont, Italy. Canadian Journal of Forest Research 35, 21-36.
50. Nanos, N., Tadesse, W., Montero, G., Gil, L., and Alia, R. (2001). Spatial stochastic modelling of resin yield from pine stands. Canadian Journal of Forest Research 31, 1140-1147.
51. Ogata, Y. and Tanemura, M. (1985). Estimation of interaction potentials of marked spatial point patterns through the maximum likelihood method. Biometrics 41, 421-433.
52. Ojansuu, R., Hynynen, J., Koivunen, J., and Luoma, P. (1991). Luonnonprosessit metsälaskelmassa (MELA)-Metsä 2000-versio. Research paper 385, Finish Forest Research Institute, Vantaa, Finland.
53. Oliver, C. D. and Larson, B. C. (1996). Forest Stand Dynamics. Wiley, New York.
54. Pacala, S. W., Canham, C. D., and Silander, J. A. (1993). Forest models defined by field measurements: I. The design of a northeastern forest simulator. Canadian Journal of Forest Research 23, 1980-1988.
55. Park, A., Kneeshaw, D., Bergeron, Y., and Leduc, A. (2005). Spatial relationships and tree species associations across a 236-year boreal mixedwood chronosequence. Canadian Journal of Forest Research 35, 750-761.
56. Paulo, M. J., Stein, A., and Tomé, M. (2002). A spatial statistical analysis of cork oak competition in two Portuguese silvopastoral systems. Canadian Journal of Forest Research 32, 1893-1903.
57. Pausa, J. G., Austin, M. P., and Noble, A. R. (1997). A forest simulation for predicting eucalyptus dynamics and habitat quality for arboreal marsupials. Ecological Applications 7, 921-933.
58. Pélissier, R. (1998). Tree spatial patterns in three contrasting plots of a southern Indian tropical moist evergreen forest. Journal of Tropical Ecology 14, 1-16.
59. Peng, C. (2000). Growth and yield models for uneven-aged stands: past, present and future. Forest Ecology and Management 132, 259-279.
60. Penttinen, A. (1984). Modelling interaction in spatial point patterns: parameter estimation by the maximum likelihood method. Jyväskylä Studies in Computer Science, Economics and Statistics, 7.
61. Penttinen, A., Stoyan, D., and Henttonen, H. M. (1992). Marked Point Processes in Forest Statistics. Forest Science 38, 806-824.
62. Pielou, E. C. (1977). Mathematical Ecology. Wiley, New York.
63. Pienaar, L. V. and Turnbull, K. J. (1973). The Chapman-Richards generalization of von Bertalanffy's growth model for basal area growth and yield in even-aged stands. Forest Science 34, 804-808.
64. Pretzsch, H. (1992). Konzeption und Konstruktion von Wuchsmodellem für Rein- und Mischbestände. Forstl Forschungsbericht 115, Univ. München.
65. Pretzsch, H., Biber, P., and Ďursk, J. (2002). The single tree-based stand simulator Silva: construction, application and evaluation. Forest Ecology and Management 162, 3-21.
66. Prévosto, B., Curt, T., Gueugnot, J., and Coquillard, P. (2000). Modelling mid-elevation Scots pine growth on a volcanic substrate. Forest Ecology and Management 131, 223-237.
67. Pukkala, T., Miina, J., Kurttila, M., and Kolström, T. (1998). A spatial yield model for optimizing the thinning regime of mixed stands of Pinus sylvestris and Picea abies. Scandinavian Journal of Forest Research 13, 31-42.
68. Rathbun, S. L. and Cressie, N. (1994). A space-time survival point process for a Longleaf pine forest in Southern Georgia. Journal of the American Statistical Association 89, 1164-1174.
69. Renshaw, E. and Ford, E. D. (1983). The interpretation of process from pattern using two-dimensional spectral analysis: methods and problems of interpretation. Journal of Applied Statistics 32, 51-63.
70. Renshaw, E. (1991). Modelling Biological Populations in Space and Time. Cambridge University Press.
71. Renshaw, E. (1997). Spectral techniques in spatial analysis. Forestry Ecology and Management 94, 165-174.
72. Renshaw, E. and Särkkä, A. (2001). Gibbs point processes for studying the development of spatial-temporal stochastic processes. Computational Statistics and Data Analysis 36, 85-105
73. Renshaw, E. (2002). Two-dimensional spectral analysis for marked point processes. Biometrical Journal 44, 1-28.
74. Renshaw, E., Mateu, J., and Saura, F. (2006). Disentangling Mark/Point Interaction in Marked Point Processes. Computational Statistics and Data Analysis. To appear.
75. Richards, F. J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany 10, 290-300.
76. Reichle, D. E. (1981). Dynamic Properties of Forest Ecosystems. Cambridge University Press, New York.
77. Ripley, B. D. (1976). The second-order analysis of stationary point processes. Journal of Applied Probability 13, 255-266.
78. Ripley, B. D. (1977). Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, B 39, 172-212.
79. Ripley, B. D. (1981). Spatial Statistics. Wiley, New York.
80. Ripley, B. D. (1988). Statistical Inference for Spatial Processes. Cambridge University Press, Cambridge.
81. Särkkä, A. and Tomppo, E. (1998). Modelling interactions between trees by means of field observations. Forest Ecology and Management 108, 57-62.
82. Särkkä, A. and Renshaw, E. (2005). The analysis of marked point patterns evolving through space and time. Computational Statistics and Data Analysis. Submitted.
83. Saura, F. and Mateu, J. (2006). Estimating mark functions through spectral analysis for marked point patterns. Communications in Statistics: Theory and Methods 35, 1-25.
84. Saura, F., Renshaw, E., and Mateu, J. (2006). Structure detection for one-dimensional patterns through wavelets. In preparation.
85. Shaw, D., Chen, J., Freeman, E. A., and Braun, D. M. (2005). Spatial and population characteristics of dwarf mistletoe infected trees in an old-growth Douglas-fir - western hemlock forest. Canadian Journal of Forest Research 35, 990-1001.
86. Shimatani, K. (2001). Multivariate point processes and spatial variation of species diversity. Forest Ecology and Management 142, 215-229.
87. Shugart, H. H. and West, D. C. (1977). Development of an Appalachian deciduous forest succession models and its application to assessment of the impact of chestnut blight. Journal of Environmental Management 5, 161-179.
88. Shugart, H. H. (1984). A Theory of Forest Dynamics. Springer-Verlag.
89. Shugart, H. H., Smith, T. M., and Post, W. M. (1992). The potential for application of individual-based simulation models for assessing the effects of global change. Annual Review of Ecology and Systematics 23, 15-38.
90. Shugart, H. H. and Smith, T. M. (1996). A review of forest path models and their application to global change research. Climatic Change 34, 131-153.
91. Simpson, E. H. (1949). Measurement of diversity. Nature 688, 163.
92. Staebler, G. R. (1951). Growth and spacing in an even-aged stand of Douglas-fir. Master's thesis. University of Michigan.
93. Stage, A. R. (1973). Prognosis model for stand development. Research Paper INT-137, USDA Forest Service.
94. Sterba, H. and Monserud, R. A. (1997). Applicability of the forest stand growth simulator PROGNAUS for the Austrian part of the Bohemian massif. Ecological Modelling 98, 23-34.
95. Stoyan, D. and Stoyan, H. (1994). Fractals, Random Shapes and Point Fields: Methods of Geometrical Statistics. Wiley, Chichester.
96. Stoyan, D., Kendall, W. S., and Mecke, J. (1995). Stochastic Geometry and its Applications. John Wiley and Sons, New York.
97. Stoyan, D. and Stoyan, H. (1998). Non-homogeneous Gibbs process models for forestry - a case study. Biometrical Journal 5, 521-531.
98. Stoyan, D. and Penttinen, A. (2000). Recent applications of point process methods in forestry statistics. Statistical Science 15, 61-78.
99. Stoyan, D. and Wälder, O. (2000). On Variograms in Point Process Statistics, II: Models of Markings and Ecological Interpretation. Biometrical Journal 42, 171-187.
100. Szwagrzyk, J. and Czerwczak, M. (1993). Spatial patterns of trees in natural forests of East-Central Europe. Journal of Vegetation Science 4, 469-476.
101. Takacs, R. (1983). Estimator for the pair potential of a Gibbsian point process. Research report 238, Johannes Kepler University, Institute für Mathematics, Linz.
102. Teck, R., Moeur, M., and Eav, B. (1996). Forecasting ecosystems with the forest vegetation simulator. Journal of Forestry 94, 7-10.
103. Tilman, D. (1988). Plant Strategies and the Dynamics and Structure of Plant Communities. Princeton University Press.
104. Tomppo, E. (1986). Models and Methods for analysing spatial patterns of trees. Communicationes Instituti Forestalls Fenniae 138.
105. Van Lieshout, M. N. M. and Baddeley, A. J. (1996). A nonparametric measure of spatial interaction in point patterns. Statistica Neerlandica 50, 344-361.
106. Van Lieshout, M. N. M. and Molchanov, I. S. (1998). Shot-noise-weighted processes: a new family of spatial point processes. Stochastic Models 14, 715-734.
107. Von Bertalanffy, L. (1949). Problems of organic growth. Nature 163, 156-158.
108. West, P. W. (2003). Tree and Forest Measurement. Springer-Verlag, Berlin.
109. Wolpert, R. L. and Ickstadt, K. (1998). Poisson/Gamma random field models for spatial statistics. Biometrika 85, 251-267.
110. Wykoff, W. R., Crookston, N. L., and Stage, A. R. (1982). User's guide to the stand Prognosis model. Technical Report INT-133, USDA Forest Service.
111. Wykoff, W. (1990). Basal area increment model individual conifers in the Northen Rock. Forest Science 36, 1077-1104.
112. Youngblood, A., Max, T., and Coe, K. (2004). Stand structure in eastside old-growth ponderosa pine forests of Oregon and northern California. Forest Ecology and Management 199, 191-217.